Worked Example 2: Verifying an Inverse
Part of Inverse Functions — GCSE Mathematics
This study notes covers Worked Example 2: Verifying an Inverse within Inverse Functions for GCSE Mathematics. Revise Inverse Functions in Algebra for GCSE Mathematics with 8 exam-style questions and 4 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 6
Practice
8 questions
Recall
4 flashcards
Worked Example 2: Verifying an Inverse
f(x) = 4x + 1. Find f⁻¹(x) and verify it's correct.
Step 1 Find the inverse
y = 4x + 1
x = 4y + 1
x - 1 = 4y
y = (x - 1)/4
f⁻¹(x) = (x - 1)/4
Step 2 Verify with f(f⁻¹(x))
f(f⁻¹(x)) = f((x-1)/4)
= 4 × (x-1)/4 + 1
= (x-1) + 1 = x ✓
Step 3 Verify with f⁻¹(f(x))
f⁻¹(f(x)) = f⁻¹(4x + 1)
= ((4x + 1) - 1)/4
= 4x/4 = x ✓